Traffic congestion is one of the most persistent problems of society today. Therefore, how to alleviate traffic congestion has always been a hot research topic in the field of traffic control, which has attracted widespread attentions [1]}.
On the freeway, when the density of traffic flow reaches a high level, the traffic flow will decrease, and the density and velocity of traffic flow will oscillate, which is called the traffic wave [2]}, i.e., the stop-and-go wave.
Traffic waves not only cause traffic jams and reduce driving comfort [3]}, [4]}, but also lead to increased fuel consumption [5]}, [6]}.
To analyze this phenomenon and study the spatiotemporal distribution characteristics of the traffic flow, macroscopic traffic modeling is used, which is particularly well suited to control design since it describes the overall spatiotemporal dynamics of the traffic flow on a freeway segment. The state variables of the macroscopic model are continuous in time and space, and they can be measured and be regulated via modern traffic management system.
Lighthill, Whitham, and Richards [7]}, [8]} proposed the LWR traffic flow model, which represents a conservation law of traffic density and describes the formation and propagation of traffic density waves on the road.
However, the oscillatory, unstable behaviors observed in the stop-and-go traffic require a higher-order model rather than the static LWR model.
The second-order Aw-Rascle-Zhang (ARZ) model proposed by Aw, Rascle, and Zhang [9]}, [10]} adds another partial differential equation (PDE) for the velocity state, which leads to a nonlinear coupled hyperbolic PDE system.
In [11]}, the authors investigated the extent to which the second-order ARZ traffic models could improve the prediction accuracy compared with the first-order LWR model.
